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feat: add stats/base/ndarray/svariance
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‎lib/node_modules/@stdlib/stats/base/ndarray/svariance/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# svariance
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> Calculate the [variance][variance] of a one-dimensional single-precision floating-point ndarray.
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<section class="intro">
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The population [variance][variance] of a finite size population of size `N` is given by
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<!-- <equation class="equation" label="eq:population_variance" align="center" raw="\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2" alt="Equation for the population variance."> -->
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```math
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\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2
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```
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<!-- <div class="equation" align="center" data-raw-text="\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2" data-equation="eq:population_variance">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/svariance/docs/img/equation_population_variance.svg" alt="Equation for the population variance.">
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<br>
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</div> -->
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<!-- </equation> -->
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where the population mean is given by
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<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->
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```math
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\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i
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```
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<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/svariance/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
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<br>
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</div> -->
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<!-- </equation> -->
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Often in the analysis of data, the true population [variance][variance] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [variance][variance], the result is biased and yields an **uncorrected sample variance**. To compute a **corrected sample variance** for a sample of size `n`,
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<!-- <equation class="equation" label="eq:corrected_sample_variance" align="center" raw="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2" alt="Equation for computing a corrected sample variance."> -->
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```math
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s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2
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```
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<!-- <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2" data-equation="eq:corrected_sample_variance">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/svariance/docs/img/equation_corrected_sample_variance.svg" alt="Equation for computing a corrected sample variance.">
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<br>
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</div> -->
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<!-- </equation> -->
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where the sample mean is given by
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<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->
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```math
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\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
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```
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<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/svariance/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
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<br>
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</div> -->
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<!-- </equation> -->
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The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample variance and population variance. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var svariance = require( '@stdlib/stats/base/ndarray/svariance' );
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```
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#### svariance( arrays )
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Computes the [variance][variance] of a one-dimensional single-precision floating-point ndarray.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var ndarray = require( '@stdlib/ndarray/base/ctor' );
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var opts = {
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'dtype': 'float32'
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};
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var xbuf = new Float32Array( [ 1.0, -2.0, 2.0 ] );
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var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
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var correction = scalar2ndarray( 1.0, opts );
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var v = svariance( [ x, correction ] );
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// returns ~4.333333
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```
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The function accepts the following arguments:
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- **arrays**: array-like object containing a one-dimensional input ndarray and a zero-dimensional ndarray specifying a degrees of freedom adjustment.
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The function assumes that the input ndarray has a single-precision floating-point data type `float32`.
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var ndarray = require( '@stdlib/ndarray/base/ctor' );
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var svariance = require( '@stdlib/stats/base/ndarray/svariance' );
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var opts = {
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'dtype': 'float32'
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};
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var xbuf = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 2 ], 1, 'row-major' );
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var correction = scalar2ndarray( 1.0, opts );
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var v = svariance( [ x, correction ] );
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// returns 6.25
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[variance]: https://en.wikipedia.org/wiki/Variance
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/ndarray/svariance/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var ndarray = require( '@stdlib/ndarray/base/ctor' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var svariance = require( './../lib' );
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// VARIABLES //
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var options = {
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'dtype': 'float32'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var correction;
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var xbuf;
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var x;
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xbuf = uniform( len, -10.0, 10.0, options );
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x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
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correction = scalar2ndarray( 1.0, options );
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return benchmark;
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function benchmark( b ) {
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var v;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = svariance( [ x, correction ] );
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if ( isnanf( v ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnanf( v ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( format( '%s:len=%d', pkg, len ), f );
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}
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}
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main();

‎lib/node_modules/@stdlib/stats/base/ndarray/svariance/docs/repl.txt‎

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{{alias}}( arrays )
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Computes the variance of a one-dimensional single-precision
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floating-point ndarray.
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Parameters
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----------
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arrays: Array<ndarray>
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Array-like object containing a one-dimensional input ndarray and a
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zero-dimensional ndarray specifying a degrees of freedom adjustment.
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Returns
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-------
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out: number
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The variance.
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Examples
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--------
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// Standard Usage:
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> var Float32Array = require( '@stdlib/array/float32' );
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> var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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> var ndarray = require( '@stdlib/ndarray/base/ctor' );
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> var xbuf = new Float32Array( [ 1.0, -2.0, 2.0 ] );
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> var x = new ndarray( 'float32', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
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> var correction = scalar2ndarray( 1.0, { 'dtype': 'float32' } );
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> {{alias}}( [ x, correction ] )
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~4.333333
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// Using ndarray properties:
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> xbuf = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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> x = new ndarray( 'float32', xbuf, [ 4 ], [ 2 ], 1, 'row-major' );
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> correction = scalar2ndarray( 1.0, { 'dtype': 'float32' } );
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> {{alias}}( [ x, correction ] )
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6.25
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See Also
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--------

‎lib/node_modules/@stdlib/stats/base/ndarray/svariance/docs/types/index.d.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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// TypeScript Version: 4.1
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/// <reference types="@stdlib/types"/>
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import { float32ndarray, typedndarray } from '@stdlib/types/ndarray';
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/**
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* Computes the variance of a one-dimensional ndarray.
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*
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* @param arrays - array-like object containing a one-dimensional input ndarray and a zero-dimensional ndarray specifying a degrees of freedom adjustment
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* @returns variance
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*
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* @example
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* var ndarray = require( '@stdlib/ndarray/base/ctor' );
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* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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* var Float32Array = require( '@stdlib/array/float32' );
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*
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* var opts = {
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* 'dtype': 'float32'
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* };
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*
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* var xbuf = new Float32Array( [ 1.0, -2.0, 2.0 ] );
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* var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
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* var correction = scalar2ndarray( 1.0, opts );
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*
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* var v = svariance( [ x, correction ] );
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* // returns ~4.333333
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*/
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declare function svariance<T extends typedndarray<number> = typedndarray<number>>( arrays: [ float32ndarray, T ] ): number;
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// EXPORTS //
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export = svariance;

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